Given:
The equation of line is
[tex]y=-\dfrac{1}{2}(x-18)[/tex]
The perpendicular line intersect the y-axis at (0,-1).
To find:
Equation of perpendicular line.
Solution:
Point slope form of a line is [tex]y-y_1=m(x-x_1)[/tex], where m is slope.
We have,
[tex]y=-\dfrac{1}{2}(x-18)[/tex]
Thus, the slope of this line is [tex]m_1=-\dfrac{1}{2}[/tex].
Product of slopes of two perpendicular lines is -1.
Let the slope of perpendicular line is [tex]m_2[/tex]. Then,
[tex]m_1\times m_2=-1[/tex]
[tex]-\dfrac{1}{2}\times m_2=-1[/tex]
[tex]m_2=2[/tex]
Slope of perpendicular line is 2 and it passes through (0,-1). So, the equation of perpendicular line is
[tex]y-(-1)=2(x-0)[/tex]
[tex]y+1=2x[/tex]
[tex]y=2x-1[/tex]
Therefore, equation of perpendicular line is [tex]y=2x-1[/tex].
